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To link to this article: http://dx.doi.org/10.1080/14685240903273881 URL: http://www.tandfonline.com/doi/abs/10.1080/14685240903273881
To cite this version: Cathalifaud, Patricia and Godard, Gilles and Braud, Caroline and Stanislas, Michel The flow structure behind vortex generators embedded in a decelerating turbulent boundary layer. (2009) Journal of Turbulence, vol. 10 (n° 42). pp. 1-37. ISSN 1468-5248
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The flow structure behind vortex generators embedded in a decelerating turbulent boundary layer P. Cathalifauda , G. Godardb , C. Braudc and M. Stanislasc∗ a Institut de M´ecanique des Fluides (UMR 5502), UPS, Universite Paul Sabatier, 18, route de Narbonne, 31062 Toulouse C´edex, France; b CORIA (UMR 6614), CNRS, Site Universitaire du Madrillet, 6801 Saint Etienne de Rouvray C´edex, France; c Laboratoire de M´ecanique de Lille (UMR 8107), EC Lille, CNRS, Boulevard Paul Langevin, Cit´e Scientifique, 59655 Villeneuve d’Ascq C´edex, France
The objective of the present work is to analyse the behaviour of a turbulent decelerating boundary layer under the effect of both passive and active jets vortex generators (VGs). The stereo PIV database of Godard and Stanislas [1, 2] obtained in an adverse pressure gradient boundary layer is used for this study. After presenting the effect on the mean velocity field and the turbulent kinetic energy, the line of analysis is extended with two points spatial correlations and vortex detection in instantaneous velocity fields. It is shown that the actuators concentrate the boundary layer turbulence in the region of upward motion of the flow, and segregate the near-wall streamwise vortices of the boundary layer based on their vorticity sign. Keywords: flow control, vortex generators, turbulent boundary layer, adverse pressure gradient, PIV, coherent structures
1. Introduction Delaying or preventing turbulent boundary layer (TBL) separation in aeronautic applications (during landing or manoeuvre of an aircraft for example) leads to enhance the lift to drag ratio and thus to fuel saving and reduction of the emitted pollution. It allows also to extend the flight envelop of an aircraft. For that purpose many actuator types were explored in the last decades over many flow configurations (flat plates, ramps, bumps, ducts, airfoils, wind turbines, etc.) [3]. Among the actuators used for that purpose, the vortex generators (VGs) were found efficient to reduce and sometimes even suppress the separated region [4]. These devices generate a streamwise vortex structure which can entrain high-momentum fluid towards the wall, hence energising the TBL, increasing quantities such as wall shear stress, turbulence intensities, momentum transfer, etc. and delaying separation. The optimal device would produce streamwise vortices just strong enough to overcome the separation without persisting within the boundary layer once the flow control objective is reached. It can be either passive or active. The resulting streamwise vortices have been subjected to many studies which helped to characterise the optimal actuator parameters and the resulting mean organisation. However, too few studies were performed on the flow re-organisation due to the difficulty to get a sufficient spatial resolution in the TBL. ∗
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Figure 1. Geometry of counter-rotating and co-rotating passive devices.
1.1. Passive VGs For passive devices, it is now well established that the strength of the vortex is driven by device parameters such as the geometry (rectangular or triangular), the height (h) relative to the boundary layer, thickness (δ) and the orientation with respect to the free-stream velocity (βpd ). When more than one device is used, the spacing between VG devices is of importance. Moreover two types of arrangements (co-rotating and counter-rotating) were found to have a rather different behaviour and thus a different control efficiency. Figures 1 and 2 give an overview of the VG parameters, L being the distance between devices of the same pair for counter-rotating arrangement and λ the distance between two pairs for counter-rotating arrangement or between devices in the co-rotating arrangement. The sign of the vortices produced by co-rotating and counter-rotating VGs can be seen on the mean velocity maps (see Figure 7). The co-rotating array transfers low and high momentum fluid together between the devices. The low momentum fluid being directed away from the wall and the high momentum towards the wall. The counter-rotating system dissociates the momentum transfer from the wall (upwash motion) and towards the wall (downwash motion). The high momentum is transported downward between devices of the same pair and upward between two pairs. For counter-rotating VGs, the boundary layer is thinned in the downwash area and thickened in the upwash area [5–7]. From the review of Lin (2002) [4] shapes such as rectangular plates or airfoils normal to the surface are optimal for the separation control purpose. A recent parametric exploration for a TBL over a bump configuration [1] found that delta-wings were more efficient than rectangular plates by 20% in term of skin friction gain and thus more efficient to achieve the control goal. In the early studies, conventional VGs with a height higher or equal to δ were first introduced [4]. However, the conventional VGs were found to produce too strong vortices which lead to a 3D organisation and additional drag compared to smaller VGs. They were rapidly replaced by smaller devices. VGs smaller than δ and even of the order of 0.2δ (embedded in the inner log region y + < 300) were still able to achieve the control of
Figure 2. Co-rotating and counter-rotating round jets vortex generators configuration.
separated flows with less associated drag than conventional VGs. Off course, the streamwise lifetime of the corresponding vortices is smaller. Lin (2002) [4] suggests that these devices should be applied close to the separation region when it is relatively fixed. The skew angle to the free stream βpd determines the vortex strength and lateral path [8]. Tilmann et al. (2002) found that increasing βpd generally increases the circulation and thus the control goal effectiveness. However, Godard and Stanislas (2006) [1] found by decreasing βpd from 23◦ to 13◦ that the vortices can be linearly strengthened up. Actually, an optimum angle of attack exists which is found equal to βpb = 18◦ by Godard and Stanislas (2006) [1] for a bump configuration. In addition, a rapid decay of the peak vorticity downstream of the VG is observed, regardless of βpb [1, 4, 7, 8]. For a defined flow configuration (TBL over a bump, ramp, airfoil, etc.), once the optimal βpb is found, there exit an optimal number of devices in the spanwise direction depending on the spanwise arrangement of the VGs and the available transverse space. Godard and Stanislas [1], by measuring the downstream wall shear stress between devices of the same pair and between two pairs of counter-rotating VGs, could perform a parametric study. They found two effects when increasing the height of the device and thus the vortex circulation. In between a pair of counter-rotating VGs, the gain in term of skin friction saturates over h = 0.2δ, whereas it still increases over h = 0.4δ between devices of the same pair. Actually, the distance between devices, for both co-rotating or counter-rotating arrangement, is of major importance [1, 4, 5, 7]. For counter-rotating arrangements, contrary to the co-rotating ones, decreasing the transverse distance between devices was found to blow-up the vortices. On the contrary, increasing too much the spacing between devices decreases the effectiveness locally [1, 5]. Departing from a non-equidistant state (λ/L = 4) Angele et al. (2005) [5] recently found, from extensive SPIV measurements, that the centres of the vortices move downstream towards an equidistant state and remain submerged in the TBL, contrary to the non-viscous theory. Therefore, the optimal spacing should be close to the equidistant state and the position of the VGs should be far enough upstream of the separation line in order for the vortices to become equidistant and to avoid back-flow in between actuators [5]. Moreover, it should be close enough to the separation line to avoid additional drag from the downstream travelling of the streamwise vortices. The optimal streamwise distance between the vortex generators line and the minimum skin friction station (or the separation line) Xvg is experienced to be Xvg / h < 100, but depending on the flow configuration (bump, ramp, airfoil, duct, etc.) [1, 4]. Note that most of the studies did not perform parametric investigations which are time consuming. The most investigated parameter is the height h of the device. Many fundamental studies were performed to analyse the organisation of the streamwise vortices produced by VGs embedded in a zero-pressure gradient (ZPG) TBL (among others [7, 9–13]). Recent studies are addressing more realistic configurations which are streamwise vortices embedded in an APG-TBL with or without separation ([1, 5, 14] among others). Indeed the flow in which the VG is embedded influences the dynamics of the produce vortices. Viscous diffusion causes the vortices to grow, the swirling velocity component to decrease and the BL to develop towards a 2D state [5]. The adverse pressure gradient is found to promote interactions between vortices hence decreasing the control effectiveness [4]. Therefore, depending on the flow configuration (flat plate within an APG, ramp, bump, etc.) the optimal parameters vary. The main flow influence is still under investigation. Logdberg et al. (2009) [7] have recently analysed the mean vortex path of longitudinal vortices produced by rectangular plates devices (or vane types) within a ZPG-TBL by means of flow visualisation and hot-wire measurements. This mean path is determined from the
maximum positive value of the mean velocity gradient tensor second invariant at different streamwise positions. For a counter-rotating array configuration of VGs, the vortices from the same pair first move away from each others. Thus, they move closer to the neighbouring vortex pair and eventually form a new counter-rotating pair with a common flow. Then the vortices move away from the wall. From the authors, this is due to the induced velocity in the upwash motion that tends to lift the vortices. Finally, they move again towards each other, closer to the equidistant-state. The authors attribute this last peculiar hook-like motion to the vortex growth and the limited space inside the boundary layer due to the neighbouring vortices. The maximum mean vortex radius is estimated to be λ/4 which implies that the mean vortex centre path is within a circle defined as followed: y/ h = 2.08; z/λ = ±0.25. Angele et al. [5] and Logdberg [14] also provide a useful rough evaluation of the vortex circulation, γ = 2khUvg /λ, where k is a coefficient that depends on the device used (k = 0.6 for vane-type VG in a ZPG configuration), and Uvg is the streamwise velocity at the tip of the device. However, this does not include the influence of the skew angle and the cross-flow organisation. The development of SPIV measurements led to further understanding of the VGs/TBL interaction. Angele et al. (2005) [5] have recently analysed the VGs/APG-TBL interaction in terms of turbulent properties. In that study the APG induce a small separation area. They found that most of the turbulence production is locally governed by one of the gradients dU/dy or dU/dz from the S-shape profile of the streamwise velocity in the x-y plane and the mushroom shape of the streamwise velocity in the y-z plane. In span, between vortices, the spanwise gradient involves significant levels of turbulence production, however the flow is overall more isotropic. 1.2.
Active VGs
Passive devices were rapidly replaced by active ones which can be turned off when not necessary in order to avoid additional drag (i.e. during cruise flight of an aircraft for instance). Many active device types were then developed for which, depending on the control source used, the control is of different nature (acoustic actuators, plasma actuators, fluidic actuators, etc.). Moreover, within fluidic actuators, one can distinguish synthetic jets devices also called Zero-Net Mass Flux [15–17] and pulsed-jet actuators [18, 19]. Indeed, for synthetic jets, contrary to pulsed-jets, there exists a suction phase. Moreover, different jet orifice shapes, orientations and operating parameters (jet oriented normal to the wall, high or low pulsating frequency, low or high velocity ratios VR between the jet exit velocity and the local free stream velocity, etc.) are used, which lead to different types of control. For instance, Greenblatt and Wygnansky [20] talk about coherent structures enhancement also called hydrodynamic control. For this control type, a low VR and a pulsating frequency adapted to the natural shedding frequency of the coherent structures is thought to be efficient. On the other hand, Raman et al. [21] are dealing with the small turbulent structures; acting one these scales is thought to allow to modify the large scale organisation more efficiently than the hydrodynamic control (no development of another dominant harmonic). The present work is focused on control studies using fluidic actuators with addition of mass to generate streamwise vortices (also called pulsed-jets actuators or pneumatic vortex generators). In continuous mode of the actuator, the streamwise evolution of the produced vortices by a single active device has been extensively analysed in ZPG configurations ([8, 22, 23] among others). The circulation and the associated strength of the vortex is modified by
parameters such as the ratio between the jet exit velocity and the local free stream velocity VR, the actuator pitch β and skew α angles and the orifice shape (see Figure 2 for notations). Contrary to passive devices, the arrangement may influence significantly the produced jet, leading to additional parameters dependency. Indeed, as highlighted in Peterson et al. [24] and Warsop et al. [25], a separation occurs within the tube (or hole) due to the supply channel flow shear at the leading or trailing edge of the hole. Warsop et al. [25] found this phenomena responsible of pressure losses up to 40% at the exit, whereas Peterson and Plesniak [24] show that for low aspect ratio of the orifice exit (less than unity), the trajectory and the spanwise spreading of the exit jet can be modified depending on the sign of the ‘supply channel-inhole flow”. Peterson and Plesniak [24] performed an extensive PIV analysis of streamwise vortices embedded in a TBL (flat plate configuration) for round jet actuators placed perpendicular to the wall. Measurements where taken in the plenum chamber and the exit hole and immediately downstream the hole. Even if the exit hole was perpendicular to the wall, this gives insight in the vortex formation mechanism. A single jet perpendicular to a wall gives rise to a pair of counter-rotating streamwise vortices, whereas two inclined jets are needed to get a qualitatively equivalent vortex pair. The origin of the remaining counter-rotating vortex pair from the jet/free stream interaction is explained by the high shear from the jet edges which induces a roll-up of the boundary layer flow. The shear is more important at the trailing edge of the hole due to bending of the jet. Behind the jet, a true wake region does not develop, but rather the action of the counter-rotating vortex pair draws the fluid away from the wall which creates a recirculation region of low velocity immediately downstream of the jet along the x-axis. When the blowing ratio increases, the jet lifts from the wall and the recirculating region is significantly reduced. Additionally, large separations occurs within the exit hole of the jet which affects the following development of the two counterrotating vortices immediately downstream the hole, when the aspect ratio of the exit hole is short (lower than 1). For instance, for a flow in the supply channel pointing in the same direction as the main flow, the counter-rotating vortices from the jet/free stream interaction are enhanced, up to 35% compared to supply channel pointing in the opposite direction to the main flow, and thus penetrates further into the TBL. Moreover, the spanwise spreading slightly decreases, when compared to supply channel pointing in the direction opposite to the main flow. When the jet has an angle to the wall (pitch and/or skew angle), two counter-rotating vortices are initially created just downstream of the device which evolves rapidly into a single coherent vortex of one sign accompanied by a much smaller and weaker region of circulation of the opposite sign near the wall [8]. The performances increase with VR and the effect is persistent far downstream from the injection (Xvg / = 200 or Xvg /δ = 40). For passive VGs, the primary vortex continues to move laterally in the direction of the vane skew, while for active VGs the path of the primary vortex is driven by VR. Consequently, too high jet exit velocity (VR) can blow the vortices out of the TBL, where it is overwhelmed by the free-stream momentum and quickly dissipates, hence reducing the control effectiveness [8]. For single VGs embedded in the TBL, the vortices are similar (at least qualitatively) to the ones from passive VGs [8, 22]. Different VGs arrangements were also investigated [2]. The sign of the produced vortices from co-rotating (CO) and counter-rotating (CT) arrangements is found similar to the passive ones. The CT active VGs are found to produce similar vortices as passive ones in the same arrangement. On the contrary, CO-active VGs merge more rapidly than passive ones and thus they dissipate more rapidly. The optimal distance between devices was found 10-times smaller than for passive devices but with a higher achievable skin friction gain. For
CT actuators, the skin friction gain is proportional to VR with little skin friction gain over VR = 3.1 for a TBL over a bump configuration without separation [2]. Hence, an optimal VR exists over which the vortices may be bleed out of the TBL which wasn’t observed by the authors. Logdberg [14] found that the necessary VR to achieve the control goal varies little with APG. With the assumption that for the same effectiveness criteria, the circulation is identical for both active and passive devices, a rough evaluation of the circulation γ for active devices was performed. Also, γ = 1.0 to 1.5 was found enough to overcome the small separation in all three APG tested. These authors also suggest that an increase of the number of jets should be preferred to improve further the control effectiveness rather than an increase of VR (in the limit of the optimal spacing). For low VR ( Q+ + Q+ the pixels are clipped at 255, where Q+ represents the mean mean mean
mean value of the positive part of Q, and Q+ mean is the corresponding standard deviation.
The result of this scaling is shown in Figure 24(b). As can be seen, the vortical elements are clearly evidence by this scaling. The next step is to select the value of the threshold. Looking at a sample of fields larger + than the one shown in Figure 24, it appears that a threshold Th∼8% of Q+ mean + Qmean (that is a grey level of 20 in the present case) is a good compromise between the amount of noise and the relevant vortical structures detected. Figure 24(c) shows the indicative function obtained from the detection functions of Figure 24(b) with this value of the threshold.
5.3. Structure extraction The last step is the extraction of the information we want (the vortices) based on the indicative function. The binary image representation of this indicative function usually
Figure 25. Example of the dilatation and erosion operations.
needs to be filtered, which may be performed using mathematical morphological functions. More information about mathematical morphology may be found in Serra [35]. As evidenced by Figure 24(c), after thresholding, noise exists in the binary images (the indicative functions) such as small structures, small holes inside structure, etc. In order to filter this noise, morphological filters were applied. The procedure used was the following: an opening (erosion + dilatation) operator followed by a closing (dilatation + erosion) operator. The opening operation smooths the contours of the structures, cuts the narrow isthmuses and suppresses the small islands and the sharp capes. On the other hand, the closing operation blocks up the narrow channels, the small lakes and the long thin gulfs. These two operations are the combination of two fundamentals operators: erosion and dilatation. Let us consider a digital image in which there is a structure X (set of pixels equals to 1), and also consider a structuring element B. The principle of the erosion and dilation operations are briefly illustrated with an example of X and B in Figure 25. The dilatation of X by B is the union of the black and shaded red pixels, and the eroded of X by B is the remaining black pixels. In the present case, different structuring element were tried. The one which seemed the most convenient was a disc of radius 1, i.e. a structuring element of the following form: 0 1 0
1 1 1
0 1. 0
Figure 24(d) shows the filtered image, obtained from the indicative functions of Figure 24(c), using the above described procedure. In order to distinguish between the positive and negative vortices, the binary images obtained were finally multiplied by the vorticity sign.
Figure 26. WAC configuration, plane 1; (a) loci of the vortex centres; (b) and (c) histograms of the number of vortex detected as a function of, respectively, z and y.
5.4. Structure characterisation The structures which remain after all the operations previously described are labelled in order to perform statistical operations on them. It is then possible to compute the average number of structures (positive and negative), the average perimeter, surface, radius, altitude, etc. The histograms of the number of structures, structures altitude and transverse positions can also be plotted. The results are presented in the next section.
5.5.
Results
5.5.1. Plane 1 In order to show the influence of jets actuation on the vortices organisation inside the boundary layer, a vortex detection was first performed for the WAC configuration. Figure 26(a) shows the loci of the vortices centres obtained by analysing the 200 velocity fields available. The red stars correspond to positive (clockwise) vortices, and the blue stars to negative (counter-clockwise) vortices. Figures 26(b) and 26(c) show the histograms of the number of vortices as a function of, respectively, the transverse and normal coordinates. The vortices are homogeneously distributed in the transverse direction, and preferably near the wall where the concentration increases strongly. Approximately four vortices of each sign were detected on the instantaneous fields, showing that the two kinds are equally probable. The average characteristics of these vortices are summarised in Table 4. These are the radius R and the intensity . The intensity is here a vorticity. The maximum (or minimum) value of the streamwise vorticity component is retained for each structure. This value is averaged over all the detected structures. The small differences between the two types of structures should be attributed to a lack of convergence. At this station, the friction velocity is uτ = 0.365, which gives R + = Ruτ /µ ∼ 73 and + = u2τ /µ ∼ 2.10−4 . The left part of Figure 27 shows the mean velocity maps, while the right part shows the loci of the centres of the vortices detected respectively in the COR and CTD configuration. We first notice that the pattern of the vortices locations is analogous to the pattern we could anticipate from the mean velocity field (left part of Figure 27), which means that the vortices generated by the jets actuation devices (which are located just upstream this plane 1) are relatively steady. For the COR configuration, around 77% of the vortices detected are positive, and the negative vortices are located between the positive ones near the wall as shown in Figure 27. Figure 28(a) shows the histogram of the number of vortices detected as a function of the transverse coordinate. This histogram exhibits five predominant transverse locations for the positive vortex, and it also confirms that negative vortices are
Figure 27. Mean velocity field and loci of the centres of the positive (red) and negative (blue) vortices; (top) COR, (bottom) CTD; plane 1.
dominant between these five locations. Figure 28(b) represents the histogram of the number of vortices detected as a function of the normal coordinate. The positive vortex are dominant around y/δ = 0.05, while the negative ones show a two peaks histogram: very near the wall (y/δ ∼ 0) and just above the positive vortices (y/δ ∼ 0.13). The average characteristics of these vortices are summarised in the Table 4. The positive vortices have a radius almost two-times larger than the negatives ones, and their intensity is 67% higher. Both vortices are stronger than the natural ones (Table 4). The positive ones are 56% larger and the negative
Figure 28. Histograms of the number of vortices detected (red: positive, blue: negative); (a) with respect to z; (b) with respect to y in the COR configuration; (c) with respect to z; (d) with respect to y in the CTD configuration; plane 1.
Table 4. Average characteristics of the vortices detected in plane 1. Config
Features
R (mm)
(rad/s)
WAC
Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices
2.97 3.09 4.66 2.39 4.14 4.16
1.72 −1.59 3.83 −2.56 2.44 −2.73
COR CTD
ones 25% smaller. The comparison of the top two images of Figure 27, together with the value of the mean radius of the positive vortices in this case (R ∼ 4.7 mm) indicates that the average velocity map of Figure 27 is in fact the result of the unsteady motion of vortices which are much smaller than what this mean map indicates. The negative vortices put in evidence by the detection procedure in the right map of Figures 27 are not at all visible in the averaged velocity map. They are slightly smaller than the vortices detected in the WAC case (Table 4). They can be either secondary vortices generated in the interaction of the actuators jets with the mean flow or negative streamwise structures from the boundary layer segregated and stretched by the actuating flow. The positive ones would then be ingested by the main actuating vortices, which would explain partly their unsteadiness so near from the actuators. For the CTD configuration (Figure 27 bottom), in addition to the two locations we could anticipate from the mean velocity field (two counter-rotating vortices), we also notice a high density of negative vortices at the left of the positive vortex, and a high density of positive vortices at the right of the negative vortex. The spatial spreading of these secondary vortices is significantly higher than that of the main ones. The histogram of Figure 28(c) confirms the existence of these two domains of vortex population close to the left and right edges of the image and around z/δ = −0.24 and z/δ = 0.24. The altitude of both the negative vortices is around y/δ = 0.05 and a bit further for the positive vortices y/δ = 0.06 as shown in the Figure 28(d). As much positive as negative vortices were detected (three of each kind on average). Table 4 summarises their mean characteristics. We can notice the similarity between the positive and negative vortices in terms of size and intensity, which constitutes the main difference compared to the COR configuration. Here, both vortices are stronger than in the WAC case.
5.5.2.
Plane 2
Figure 29(a) shows the loci of the centres of the detected vortices for the WAC configuration, while Figure 30 gives the same data for the COR, CTD, CTU and PADb configurations. Figures 29(b), 29(c), 31 and 32 give the corresponding histograms. In the WAC case, the distribution is still equiprobable and homogeneous in z, but the wall region, where the population is high, has extended significantly away from the wall. This is clearly seen both in Figures 29(b) and 29(c). Table 5 gives the mean characteristics. The radius has increased by about 20% and the intensity has diminished by the same percentage as compared to plane 1. A higher concentration of positive vortices is observed in the COR configuration compared to the WAC case. These positive vortices are especially dominant on the left part of the field (z/δ < 0.16). The histograms of Figure 31(a)–32(a) confirm the dominance of these positive vortices in the region where the large scale motion has been
Figure 29. (a) Loci of the centres of vortices detected in the WAC configuration; (b) histogram with respect to z; (c) histogram with respect to y; plane 2.
Figure 30. Loci of the centres of vortices detected (red: positive, blue: negative); (a) COR, (b) CTD, (c) CTU, (d) PADb; plane 2.
Figure 31. Histograms with respect to z of vortices detected; (a) COR, (b) CTD (c) PADb; plane 2.
Figure 32. Histograms with respect to y of vortices detected; (a) COR, (b) CTD, (c) PADb; plane 2.
previously identified (Figure 19). In the COR configuration, we detected 75% more positive than negative vortices (about 7 positives and 4 negatives on each instantaneous field). Table 5 gives the mean characteristics of these vortices. Their intensity has significantly decreased as compared to plane 1 and is now comparable, for both signs, to the WAC case in plane 2. The positive vortices have decreased in size, while the negative ones have increased, compared to plane 1, but a difference still exists in plane 2 between both signs. In the CTD configuration (Figure 30(b)), a concentration of positive vortices can be distinguished around z/δ = −0.18 , and of negative vortices around z/δ = 0.18 (see Figure 30(b) and Figures 31(b)–32(b)). A deficit of vortices is observed at the centre of the image, which corresponds to the downwash zone. Vortices of opposite sign gather near the wall and on each side of the origin and to a less extent, outside and above the main vortex (z/δ = ±0.24, y/δ = 0.16). In the CTU configuration, the opposite behaviour is obtained, with a concentration of vortices at the centre of the field (positive vortices around z/δ = −0.13 and negative vortices around z/δ = 0.13), which is an upwash zone, and a deficit of vortices at the left and right edges (downwash zones). The mean characteristics are given in Table 5 for the CTD and for the CTU. First, the agreement appears fairly good between the two configurations which correspond to the same flow at different transverse location. The vortices are slightly smaller than in plane 1 (about 10% on the radius) and comparable to the positive vortices of the COR case. Their intensity has decreased significantly (by about 50%) and is now comparable to that of the WAC and COR vortices. The PADb configuration is quite similar to the CTD one (see Figures 30(d) and 31(c)– 32(c)). However, it can be noticed that the transverse location of the positive vortices concentration is around z/δ = −0.16 and around z/δ = 0.16 for the negative vortices. Consequently, the downwash zone between these two concentrations is narrower than in the Table 5. Average characteristics of the vortices detected in plane 2. Config
Features
R (mm)
(rad/s)
WAC
Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices
3.55 3.54 3.90 3.247 3.79 3.82 3.84 3.83 4.048 4.22
1.35 −1.39 1.32 −1.32 1.48 −1.45 1.33 −1.33 1.47 −1.60
COR CTD CTU PADb
Figure 33. Loci of the centres of vortices detected (red: positive, blue: negative); (a) WAC, (b) COR, (c) CTD, (d) PADb; plane 3.
CTD configuration and the secondary counter-rotating vortices close to the wall are less numerous. The second area of secondary counter-rotating structures (around z/δ = ±0.24, y/δ = 0.16) is also visible. As a summary, it can be said that although the actuating vortices still drive the global structure of the flow, the detected vortices in this plane have evolved to a size and intensity which is not far from the case without actuation. The different cases are thus distinguished mainly by the spatial distribution of the vortices of both sign, which are evenly distributed in span in the WAC case and are segregated more or less differently by the different actuators. 5.5.3. Plane 3 Figure 33 shows the loci of the centres of the detected vortices in the WAC, COR, CTD and PADb configurations. Their average characteristics are given in Table 6. Figure 34 shows Table 6. Average characteristics of the vortices detected in plane 3. Config
Features
R (mm)
(rad/s)
WAC
Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices Positive vortices Negative vortices
5.01 4.94 4.79 4.41 4.84 4.59 5.12 5.00
1.61 −1.44 1.37 −1.28 1.69 −1.40 1.55 −1.40
COR CTD PADb
Figure 34. Histograms with respect to z of vortices detected; (a) WAC, (b) COR, (c) CTD, (d) PADb; plane 3.
Figure 35. Histograms with respect to y of vortices detected; (a) WAC, (b) COR, (c) CTD, (d) PADb; plane 3.
the histograms of the number of vortices detected as a function of the transverse coordinate in the same configurations and Figure 35 the histograms in the wall normal direction. The differences between all four configurations are much less evident than in the first two planes. At this station, turbulent diffusion has strongly acted to distribute the vortices over the whole field of view. The WAC case is still homogeneous along z. The slight excess of positive vortices near the wall should be attributed to a lack of convergence. The vortical region is much wider than in the upstream planes. It extends now to y/δ ∼ 0.25. The two concentrations of positive and negative vortices can still be clearly distinguished in the PADb configuration (see the corresponding histogram in Figure 34). They are less evident in the CTD case. The COR configuration still exhibits an excess of positive vortices on the left part of the image. In all the actuated cases, a higher concentration of positive vortices is observed near the wall, especially in the COR configuration (see the histograms in Figure 34). Actually, for the COR configuration, 58% more positive than negative vortices are detected. Like in plane 2, the size and intensity of the vortices in the actuated cases are comparable to the WAC configuration. The intensity of the negative vortices is slightly smaller than that of the positive ones in all cases, including WAC. This result should thus be taken with caution and attributed, for the moment, to a lack of convergence. Compared to plane 2, the size of the vortices has slightly increased, which is not surprising, but their intensity has increased too, which is more difficult to explain. To summarise, in this plane, which is far downstream of the actuators (Xd/ h = 57, Xd/ = 170), the vortical actuating flow has strongly mixed with the boundary layer turbulence and it becomes difficult to distinguish the actuating vortices in the instantaneous velocity maps. Nevertheless, as was shown by Godard and Stanislas [1, 2], the actuation is still fairly efficient on average when looking at the wall friction.
5.6. Discussion and conclusion As was shown by the above results, the analysis of the vortical structure of the flow in planes normal to the wall and to the mean flow are quite instructive on the actuating flow organisation. The streamwise vortices generated by the different actuators are initially fairly localised in space and have a size and intensity different from the boundary layer turbulence. When developing downstream, they strongly reorganise the near-wall vorticity, but they seem to fairly rapidly adapt themselves in size and intensity to the surrounding turbulence. Two explanations can be given to this observation: in a first scenario, the actuating vortices observed clearly in plane 1 reduce in size and in intensity to mix themselves with the existing turbulent streamwise eddies. In a second scenario, the actuating vortices grow rapidly in size so that they cannot be individualised in the turbulent background. But, they are strong
Figure 36. Mean indicative function; CTD configuration; (a) plane 1, (b) plane 2, (c) plane 3.
Figure 37. Mean indicative function; (a) PADb configuration, plane 2; (b) PADb configuration, plane 3; (c) WAC configuration, plane 3.
enough to organise and segregate globally the near-wall streamwise vortices of the natural boundary layer. This second scenario is somewhat supported by the results shown in Figures 36 and 37. These figures show the mean value of the indicative functions, averaged over the number of samples for the different configurations and in the different planes. This parameter is, in some way, a spatial probability of detecting a vortex. As shown by Figure 36(a), in plane 1 for the CTD configuration, this function is well localised at the place where the mean actuating vortex appears on the mean velocity map. Figures 36(b) and 37(a) show the same parameter in plane 2 for the CTD and PADb configurations. Obviously, the size of the most probable areas is much larger than the size of the individual vortices detected and comparable to the size of the average vortex evidenced in Figure 18 for example. The value of the function in the most probable area has also decreased significantly, in agreement with the spreading of the vortices location observed above. Comparable conclusion can be drawn by looking at Figures 36(c) and 37(b). The comparison of Figures 37(b) and 37(c) clearly shows that in plane 3, apart for the size of the vortical region, it becomes difficult to distinguish between the PADb and WAC cases. 6.
General conclusion
The aim of the present study was to push further the analysis of the PIV data recorded by Godard and Stanislas [1, 2] on different actuating flow situations in order to try to better understand the physics of the flow. Measurements were available in three planes normal to the flow, downstream of the actuators and for smooth wall, passive and round jets actuators. Godard and Stanislas [1, 2] did plot only mean velocity maps out of their PIV data. In the present contribution, some mean velocity profiles were plotted to complement these maps. These profiles emphasise the difference between the co- and counter-rotating configurations and clearly show that the actuation effect is mostly due to a downwash of high momentum fluid towards the wall. To go into more details, the turbulent kinetic energy maps were plotted, then some relevant double spatial correlation coefficients maps and, finally, the individual vortices were detected and characterised in each PIV instantaneous map. The analysis of these data confirm the difference between the co- and counter-rotating cases. With the co-rotating round jets, the actuating vortices, which are individually visible in plane 1, just downstream of the actuators, merge rapidly to form a large vortical region, which shows a global coherence on the correlation maps, which moves transversely by self-induction. This large vortical region concentrates a significant amount of turbulent kinetic energy and preferably vortices of the same sign. It shows also a global excess of streamwise velocity with respect to the non-actuated case, indicative of its efficiency. This efficiency was evidenced by Godard and Stanislas [1, 2] with wall shear stress measurements.
The counter-rotating actuators (both passive and round jets) generate stable counterrotating streamwise vortices which stay coherent and individualised far downstream. These vortices are much stronger than the natural boundary layer vortices in plane 1 but they appear to progressively grow in size, reduce in intensity and mix themselves in the BL turbulence. They appear to segregate spatially this turbulence, concentrating the turbulent kinetic energy in the upwash regions. They also segregate the BL streamwise vortices, based on their sign, gathering them in different regions in space. From the evolution observed in the three measurement planes, it can be expected that these actuating vortices progressively disappear downstream, but this may take a fairly long distance.
Acknowledgements The research reported here was undertaken as part of the AEROMEMS II project (Advanced Aerodynamic Flow Control Using MEMS, Contract No G4RD-CT-2002-00748). The AEROMEMS II project was a collaboration between BAE SYSTEMS, Dassault, Airbus Deutschland GmbH, EADSMilitary, Snecma, ONERA, DLR, LPMO, Manchester University, LML, Warwick University, TUB, Cranfield University, NTUA, and Auxitrol. The project was funded by the European Union and the project partners. Part of the work was also performed in the frame of CISIT.
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